Inverse kinematics bone doesn't stick to its source
I think that 


your IK could be too short. The video you are following use another bone above that with the IK constraint.
this does not allow you to replicate what he's doing in the video: he grabs the IK target but he doesn't moves it too far from the chain. 


To find out, try to 


remove the IK constraint from the bone "bone"
select the bone "bone", and subdivide it (press "w" > subdvide)
now you have 2 bones above the IK target bone
select the new bone, that is now directly attached to the IK target (it should be named "bone.001"
reapply the same IK constraint to the IK target as it was before
now grab the IK target and move it around: it stays with the constrained bone. 
however, if you move the IK target too far, the constrained bone can't "stay" with it and they separate until the IK target is too far...